The leader of the Northern Irish party propping up Britain's minority government said on Tuesday her party was just as firm about its demands for a Brexit plan for Northern Ireland as Ireland's government.
At the 14-15 December summit, European leaders will decide whether enough progress has been made in the negotiations on Ireland, the UK's "divorce bill" and citizens' rights so far to open trade talks.
A deal fell apart on Monday when the UK's pledge of "regulatory alignment" across Ireland - to avoid border customs checks and posts - was vetoed by the DUP.
"Logically that will happen once we have confirmation that we have reached "sufficient progress" and are going to begin the phase two process with the European Union", he said.
Commission chief Jean-Claude Juncker's chief of staff Martin Selmayr tweeted a picture of white smoke - the sign used by the Vatican to signify the election of a new pope - shortly after May's arrival.
The British Prime Minister is apparently close to finalising a new deal, and is seeking approval from the Northern Irish DUP and Irish Prime Minister Leo Varadkar.
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The identity of the shooter has yet to be released. "No other injuries reported", the police said. The attack took place at Aztec High School, New Mexico State Police said on Twitter.
Theresa May will put forward a fresh offer to solve the Irish border dispute within hours, as the EU's Brexit negotiator said Friday was the deadline to rescue a deal.
"In Northern Ireland we guarantee there will be no hard border", May told a press conference with Juncker.
After talks in Dublin, Irish Taoiseach Leo Varadkar and Dutch PM Mark Rutte made clear the European Union would not compromise and allow the Irish border to be kicked down the road to phase two of the talks, even under threat of Britain crashing out with no deal or divorce negotiations dragging on to 2018.
However, the Democratic Unionist Party signalled that it believed a deal was still some way off - with Arlene Foster, the DUP leader, yet to have face-to-face talks with Ms May.
The Government continues to insist it will not change the substance of what it says was agreed with the British government on Brexit earlier this week. Mr Varadkar said the decision to proceed to the next phase may not be taken until the new year.
"The sooner we are in control over our own future here in Scotland the better, and this week has proved it", she added.
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